The ultraviolet (UV) band edge photorefractivity of Sn-doped ${\mathrm{LiNbO}}_3$ (LN:Sn) at $325\mathrm{nm}$ has been investigated. A sharp decrease of beam distortion, which is accompanied by a significant increase in the photoconductivity, is observed in LN:Sn crystals with Sn-doping concentrations at or above $2.0\mathrm{mol}\%$ . The diffraction efficiency, the holographic recording sensitivity and response rate, and the two-wave coupling gain coefficient are greatly enhanced when the Sn-doping concentration reaches $2.0\mathrm{mol}\%$ or more. Unlike ${\mathrm{LiNbO}}_3$ doped with Hf in which the UV gratings can be erased easily by a red beam, the UV gratings in LN:Sn can withstand long-term red beam illumination. Electrons are determined to be the dominant light-induced charge carriers responsible for the UV band edge photorefraction. The observed enhancement on the UV band edge photorefractivity is found to be associated with the showup of an absorption band around $325\mathrm{nm}$ in LN:Sn crystals with Sn-doping concentrations at or above $2.0\mathrm{mol}\%$ .